Per NFL.com's Gregg Rosenthal, Dorsey said the Browns' door is "wide-open" to deal the No. 1 overall pick.
"Give me a call and see what's up," he said.
Cleveland secured the No. 1 overall pick after going 0-16 last season. It added the Houston Texans' first-round pick last year when the Texans moved up 13 spots to select Deshaun Watson.
Predraft prognostications have the Browns selecting a quarterback with their first pick. B/R's Matt Miller has USC star Sam Darnold going to Cleveland at No. 1 overall in his most recent mock draft.
The Browns would also have the luxury of using the No. 4 pick on a quarterback if that's the direction they choose to go. Darnold, UCLA's Josh Rosen, Wyoming's Josh Allen and Oklahoma's Baker Mayfield are all potential first-round talents.